Summary: A Hybrid Noncooperative Game Model
for Wireless Communications
Tansu Alpcan 1 and Tamer Bas¸ar 1
Abstract
We investigate a hybrid noncooperative game motivated by the practical problem of joint power control and base station
(BS) assignment in code division multiple access (CDMA) wireless data networks. We model the integrated power control
and BS assignment problem such that each mobile user's action space not only includes the transmission power level but also
the respective BS choice in order to obtain further optimizations. Users are associated with specific cost functions consisting
of a logarithmic user preference function in terms of service levels and a linear pricing scheme to enhance the overall system
performance by limiting interference and to preserve battery energy. We study the existence and uniqueness properties of
Nash equilibrium solutions of the hybrid game, which constitute the operating points for the underlying wireless network.
Since this task cannot be accomplished analytically even in the simplest cases due to the nonlinear and complex nature of the
cost and reaction functions of mobiles, we conduct the analysis numerically using grid methods and randomized algorithms.
Finally, we simulate a dynamic BS assignment and power update scheme, and compare it with "classical" noncooperative
power control algorithms in terms of aggregate SIR levels obtained by users.
I. INTRODUCTION
The primary objective of mobile users in wireless networks is to achieve and maintain a satisfactory level of service,
which may be described in terms of signal-to-interference ratio (SIR). The mobiles may vary their uplink transmission
power levels and connections to the base stations in order to reach this goal. Since in code division multiple access (CDMA)
systems signals of other users can be modeled as interfering noise signals, each mobile degrades the level of service of